BK was investigated, according to the linked source, beginning on January 10, 2023. It may have been a very thorough and convincing (but not entirely revealed) investigation that proved BK's lack of involvement in the 2021 incident, but this particular article leaves some room for doubt to creep in, in my view.
Is there a link somewhere indicating BK did not like to fly? Trying to remember if I've heard that. We know he motored across the country to WSU and back to PA, but I don't recall if not liking to fly was one of the reasons behind his choice.
"The investigation of Kohberger was brief, however, and shut down nine days later when the Graduate Program Coordinator informed Sgt. Engle that there was no record of the future criminology student attending any campus events that weekend.
Police did not appear to look into the possibility of Kohberger going on a non-sanctioned visit that weekend, which would have been while he was enrolled at DeSales University in Pennsylvania."
Bryan Kohberger became a possible suspect because of the similarities between this thwarted attack and the murders of four University of Idaho students 10 miles away
people.com